Project Euler 389 - Platonic Dice

Official link: https://projecteuler.net/problem=389

Thought Process

Note: This problem is not suitable for hints!!!

If you're struggling with this problem have a look at the following pages:

1. https://en.wikipedia.org/wiki/Variance

2. https://en.wikipedia.org/wiki/Probability-generating_function

I promise you that, somewhere, in these both pages there is a way to solve the problem. I personally did it using the 2nd link, but after seeing other peoples solution the first one is probably less work and easier to understand.

Now onto the problem.

I did a problem a long time ago relating to the Sicherman Dice and since then have been waiting for an opportunity to use the solution method mentioned in the wiki, and in the end I ended up doing the entire problem on pen and paper, not a single line of code.

First I'll briefly explain the method that the wiki shows